We revisit the SeqBin constraint. This meta-constraint subsumes a number of important global constraints like Change, Smooth and IncreasingNValue. We show that the previously proposed filtering algorithm for SeqBin has two drawbacks even under strong restrictions: it does not detect bounds disentailment and it is not idempotent. We identify the cause for these problems, and propose a new propagator that overcomes both issues. Our algorithm is based on a connection to the problem of finding a path of a given cost in a restricted $n$-partite graph. Our propagator enforces domain consistency in O(nd^2) and, for special cases of SeqBin that include Change, Smooth and IncreasingNValue, in O(nd) time.

Combinatorial optimization is widely applied in a number of areas nowadays. Unfortunately, many combinatorial optimization problems are NP-hard which usually means that they are unsolvable in practice. However, it is often unnecessary to have an exact solution. In this case one may use heuristic approach to obtain a near-optimal solution in some reasonable time. We focus on two combinatorial optimization problems, namely the Generalized Traveling Salesman Problem and the Multidimensional Assignment Problem. The first problem is an important generalization of the Traveling Salesman Problem; the second one is a generalization of the Assignment Problem for an arbitrary number of dimensions. Both problems are NP-hard and have hosts of applications. In this work, we discuss different aspects of heuristics design and evaluation. A broad spectrum of related subjects, covered in this research, includes test bed generation and analysis, implementation and performance issues, local search neighborhoods and efficient exploration algorithms, metaheuristics design and population sizing in memetic algorithm. The most important results are obtained in the areas of local search and memetic algorithms for the considered problems. In both cases we have significantly advanced the existing knowledge on the local search neighborhoods and algorithms by systematizing and improving the previous results. We have proposed a number of efficient heuristics which dominate the existing algorithms in a wide range of time/quality requirements. Several new approaches, introduced in our memetic algorithms, make them the state-of-the-art metaheuristics for the corresponding problems. Population sizing is one of the most promising among these approaches; it is expected to be applicable to virtually any memetic algorithm.

The multiple attribute mixed type decision making is performed by four methods, that is, the relative approach degree of grey TOPSIS method, the relative approach degree of grey incidence, the relative membership degree of grey incidence and the grey relation relative approach degree method using the maximum entropy estimation, respectively. In these decision making methods, the grey incidence degree in four-dimensional Euclidean space is used. The final arrangement result is obtained by weighted Borda method. An example illustrates the applicability of the proposed approach.

Hidden Markov Models (HMMs) are one of the most fundamental and widely used statistical tools for modeling discrete time series. In general, learning HMMs from data is computationally hard (under cryptographic assumptions), and practitioners typically resort to search heuristics which suffer from the usual local optima issues. We prove that under a natural separation condition (bounds on the smallest singular value of the HMM parameters), there is an efficient and provably correct algorithm for learning HMMs. The sample complexity of the algorithm does not explicitly depend on the number of distinct (discrete) observations---it implicitly depends on this quantity through spectral properties of the underlying HMM. This makes the algorithm particularly applicable to settings with a large number of observations, such as those in natural language processing where the space of observation is sometimes the words in a language. The algorithm is also simple, employing only a singular value decomposition and matrix multiplications.

The restricted Boltzmann machine (RBM) is a flexible tool for modeling complex data, however there have been significant computational difficulties in using RBMs to model high-dimensional multinomial observations. In natural language processing applications, words are naturally modeled by K-ary discrete distributions, where K is determined by the vocabulary size and can easily be in the hundreds of thousands. The conventional approach to training RBMs on word observations is limited because it requires sampling the states of K-way softmax visible units during block Gibbs updates, an operation that takes time linear in K. In this work, we address this issue by employing a more general class of Markov chain Monte Carlo operators on the visible units, yielding updates with computational complexity independent of K. We demonstrate the success of our approach by training RBMs on hundreds of millions of word n-grams using larger vocabularies than previously feasible and using the learned features to improve performance on chunking and sentiment classification tasks, achieving state-of-the-art results on the latter.

We present a domain-independent algorithm that computes macros in a novel way. Our algorithm computes macros "on-the-fly" for a given set of states and does not require previously learned or inferred information, nor prior domain knowledge. The algorithm is used to define new domain-independent tractable classes of classical planning that are proved to include \emph{Blocksworld-arm} and \emph{Towers of Hanoi}.

The feature of our method different from other fuzzy grey relation method for supermixed multiple attribute group decision-making is that all of the subjective and objective weights are obtained by interval grey number and that the group decisionmaking is performed based on the relative approach degree of grey TOPSIS, the relative approach degree of grey incidence and the relative membership degree of grey incidence using 4-dimensional Euclidean distance. The weighted Borda method is used to obtain final rank by using the results of four methods. An example shows the applicability of the proposed approach.

A new generalized multilinear regression model, termed the Higher-Order Partial Least Squares (HOPLS), is introduced with the aim to predict a tensor (multiway array) $\tensor{Y}$ from a tensor $\tensor{X}$ through projecting the data onto the latent space and performing regression on the corresponding latent variables. HOPLS differs substantially from other regression models in that it explains the data by a sum of orthogonal Tucker tensors, while the number of orthogonal loadings serves as a parameter to control model complexity and prevent overfitting. The low dimensional latent space is optimized sequentially via a deflation operation, yielding the best joint subspace approximation for both $\tensor{X}$ and $\tensor{Y}$. Instead of decomposing $\tensor{X}$ and $\tensor{Y}$ individually, higher order singular value decomposition on a newly defined generalized cross-covariance tensor is employed to optimize the orthogonal loadings. A systematic comparison on both synthetic data and real-world decoding of 3D movement trajectories from electrocorticogram (ECoG) signals demonstrate the advantages of HOPLS over the existing methods in terms of better predictive ability, suitability to handle small sample sizes, and robustness to noise.

Sequential Monte Carlo techniques are useful for state estimation in non-linear, non-Gaussian dynamic models. These methods allow us to approximate the joint posterior distribution using sequential importance sampling. In this framework, the dimension of the target distribution grows with each time step, thus it is necessary to introduce some resampling steps to ensure that the estimates provided by the algorithm have a reasonable variance. In many applications, we are only interested in the marginal filtering distribution which is defined on a space of fixed dimension. We present a Sequential Monte Carlo algorithm called the Marginal Particle Filter which operates directly on the marginal distribution, hence avoiding having to perform importance sampling on a space of growing dimension. Using this idea, we also derive an improved version of the auxiliary particle filter. We show theoretic and empirical results which demonstrate a reduction in variance over conventional particle filtering, and present techniques for reducing the cost of the marginal particle filter with N particles from O(N2) to O(N logN).

We consider the problem of learning Bayesian network classifiers that maximize the marginover a set of classification variables. We find that this problem is harder for Bayesian networks than for undirected graphical models like maximum margin Markov networks. The main difficulty is that the parameters in a Bayesian network must satisfy additional normalization constraints that an undirected graphical model need not respect. These additional constraints complicate the optimization task. Nevertheless, we derive an effective training algorithm that solves the maximum margin training problem for a range of Bayesian network topologies, and converges to an approximate solution for arbitrary network topologies. Experimental results show that the method can demonstrate improved generalization performance over Markov networks when the directed graphical structure encodes relevant knowledge. In practice, the training technique allows one to combine prior knowledge expressed as a directed (causal) model with state of the art discriminative learning methods.